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A police chief wants to determine if crime rates are different for four different areas of the city (East, West, North, and South sides), and obtains data on the number of crimes per day in each area. To test the null hypothesis that all population mean crime rates are equal, use the one-way ANOVA table shown below. At the 0.05 level of significance, we

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Source of Variation & SS & df & MS & F & Critical Value & p-value \\
\hline
Treatment & 26.484 & 3 & 8.828 & 275 & & 0.0697 \\
\hline
Error & 64.17 & 20 & 3.21 & & & \\
\hline
Total & 151.96 & 23 & & & & \\
\hline
\end{tabular}

Select one:
A. Reject the null hypothesis; therefore, concluding that we have evidence that the average number of crimes differ by the area of the city.
B. Do not reject the null hypothesis; therefore, concluding we have no evidence that the average number of crimes differ by the area of the city.
C. Do not reject the null hypothesis; therefore, concluding that we have evidence that the average number of crimes differ by the area of the city.
D. Reject the null hypothesis; therefore, concluding we have no evidence that the average number of crimes differ by the area of the city.

Sagot :

GinnyAnsweridn
To solve this problem, let's go through the steps required to perform a one-way Analysis of Variance (ANOVA) and interpret the results based on the provided table.

1. State the Hypotheses:
- Null Hypothesis (H0): The population mean crime rates are the same for all four areas of the city.
- Alternative Hypothesis (H1): At least one area's mean crime rate is different from the others.

2. Given Information:
- F-value: 275
- p-value: 0.0697
- Level of significance (α): 0.05
- Degrees of freedom for treatment (df between groups): 3
- Degrees of freedom for error (df within groups): 20

3. Decision Rule:
- If the p-value < α (0.05), reject the null hypothesis (H0).
- If the p-value > α (0.05), do not reject the null hypothesis (H0).

4. Compare the p-value with α:
- In this case, the p-value is 0.0697.
- The level of significance (α) is 0.05.

5. Make the Decision:
- Since 0.0697 > 0.05, we do not reject the null hypothesis (H0).

6. Conclusion:
- We do not reject the null hypothesis. Therefore, we conclude that we have no evidence to suggest that the average number of crimes differs by the area of the city.

Given the above steps, the correct answer is:

Do not reject the null hypothesis; therefore, concluding we have no evidence that the average number of crimes differ by the area of the city.
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